By strange coincidence, a week after I meet Rachel Unthank, her sister Becky, and the rest of her group the Winterset, in a beautiful old farm cottage near the village of Corbridge, outside Newcastle, I am sitting with Robert Wyatt in his house in Louth, Lincolnshire. We are listening to Felton Lonnin, the traditional song that opens The Bairns, the Winterset's new album. There is something incomparably magical about listening to a piece of music you love with someone else, particularly someone for whom you also have huge respect and affection. I watch Wyatt's face as he negotiates the contours of the song: the flinty voices of sisters Rachel and Becky Unthank, the gentle, unexpectedly jazz-inflected chords of pianist Belinda O'Hooley's supremely subtle accompaniment, the rolling strings, the beat measured out by the tap of Rachel's shoe. Wyatt is enchanted. It is traditional folk music, but with a brave new cast.

Then we listen to their version of Sea Song, originally from Wyatt's 1974 solo debut Rock Bottom. He has repeatedly commented on the courage of anyone prepared to take on the complexity of his songs. As the sisters' harmonies die away, Wyatt, visibly impressed, says: "That's the best version of that I've heard."

Released in 2005 on the tiny Rabble Rouser label, Cruel Sister, the Winterset's debut, garnered instant and widespread acclaim, culminating in Mojo magazine's folk album of the year award; the album sold more copies in the month following the Mojo award than in the six months preceding it.

Though eight years separate Rachel, 30, and Becky, they have a closeness that's reflected in their intuitive sense of harmony. Their pale skin and long, dark hair reflect a little of the gothic quality of their fabulous surname, and it is easy to imagine them as the twin heroines of some strange Poe fantasy. In person though, they are funny, ribald company - hardly the comparatively austere presences that haunt their recordings - and laugh when asked about something as serious-sounding as their folk heritage. "Me and Becky were indoctrinated from birth," Rachel says. "We always went to folk festivals, from when we were young."

Their father sang in a group called the Keelers (after the boatmen who sailed up and down the Tyne), and their mother had always sung. "My dad's in a rapper [sword] dance team," adds Rachel. "Me and Becky did clog dancing too."

"From when we were four or five," Becky continues her sister's sentence in the way close siblings do. "We went round festivals doing clog dancing before we were singing."

"Our family parties are like a sing-song too," adds Rachel, "It's the law."

Then it's back to Becky again: "Everyone goes round the room and has a sing."

Growing up, the girls remember hearing the Watersons, June Tabor and Richard Thompson's Morris On album, a record, considered radical on its release in 1972, of Morris-dancing tunes. "Mum and Dad would get up in the morning on the weekend and put on Morris On and go back to bed," remembers Rachel, "and we'd dance around the living room. We were always surrounded by live singing at folk clubs and festivals. We did listen to records, but when I think back it's the live singing I remember more: all kinds of different singers, often I wouldn't know who they were, but they were all telling stories."

More than the act of singing, it was the songs' strong narrative thread that caught their imagination. "The stories were the thing," says Rachel. "We listened to a lot of storytellers too."

"One of my best friends' dad is a storyteller," continues Becky. "Storytelling festivals are a big thing in the folk world. Lots of kids go."

"It's like a magical world," says Rachel, a 30-year-old woman who still has the palpable excitement of a child.

Growing up, the girls "learned to sing in the car, really, to occupy ourselves", Rachel remembers. "It's always been a really big part of our lives." Becky: "I was too shy to sing on my own, 'cos I was little, so we all sang together."

Rachel started performing solo from around the age of 17; when she was 21 her sister joined her, and they remained a duo for some time. Adrian McNally, who manages the group, runs the label and produced both Cruel Sister and The Bairns, only helped the sisters to find other musicians when making an album seemed like a realistic prospect. They began with a pianist, Belinda O'Hooley, whose background was in folk but whose career had taken her elsewhere.

While at college in Hull, O'Hooley's summers had been spent in Sligo, playing on the traditional music scene with her Irish Catholic father. To pay her way in England, she began singing in nursing and residential homes, doing two shows a day, singing standards from "the 1920s and 30s mainly, and learning songs from the oldies. It was a great way to practise."

O'Hooley, 36, is a droll, handsome woman, whose camp vaudevillian asides provide the perfect between-song tonic when the Winterset play live. She has also something that could be considered a dark secret in the serious world of traditional folk: "I was on Stars in Their Eyes as Annie Lennox; that's how Adrian knew me. He was a cabaret agent. As well as playing in a Robbie Williams tribute band." Everyone hoots with laughter.

"We were called No Regrets," says McNally, with the glum resignation of a man who knows the cat is out of the bag. "There was already one called Robbing Williams."

It is the jazz chords O'Hooley learned from the Tin Pan Alley standards she was playing, together with the unexpected choice of repertoire - apart from Robert Wyatt's Sea Song, The Bairns includes a fragment of Bonnie "Prince" Billy's A Minor Place - that sets the Winterset apart. Indeed, all the musicians involved, including the fourth member, violinist Niopha Keegan, 31, strive to avoid anything recognisable as folk cliche.

That said, both sisters revel in the rich, thriving local folk tradition. "We're very lucky in the north-east that it does thrive," says Becky. What used, literally, to be a working tradition - songs sung by miners and shepherds - has survived in large part thanks to the work of Alistair Anderson. Anderson is the artistic director of Folkworks, a centre for the promotion and development of folk music in the north of England, now part of the Sage in Gateshead. He also helped set up the four-year, performance-based folk degree, through which the band found Keegan. It's the only one in England, though there are similar degrees in Ireland (run by Keegan's brother, incidentally), Scotland and mainland Europe.

The Unthanks' love of traditional singing and storytelling is brought up to date by O'Hooley's two original songs, particularly Whitethorn, a harrowing piece Rachel admits she was initially "scared to sing".

"It's about my great-grandmother, struggling to survive in a tiny village in Ireland," O'Hooley explains. "She was pregnant 15 or 16 times and only two babies survived. Because they hadn't lived long enough to be christened, they weren't buried in the local churchyard, but under a whitethorn bush, actually near where my dad lives now. It really brought home to me the history of women's struggles, and made me want to write."

"There was a responsibility in singing it," says Rachel. "[When we started to make albums] I really didn't want to lose the traditional singing aspect and the storytelling. All I ever really wanted to be was a folk singer."